$x+3=2x+8-2\sqrt{ 2x+8 }+1$
Add the numbers$x+3=2x+9-2\sqrt{ 2x+8 }$
Move the expression to the left-hand side and change its sign$x+3+2\sqrt{ 2x+8 }=2x+9$
Move the expression to the right-hand side and change its sign$2\sqrt{ 2x+8 }=2x+9-x-3$
Collect like terms$2\sqrt{ 2x+8 }=x+9-3$
Subtract the numbers$2\sqrt{ 2x+8 }=x+6$
Square both sides of the equation$4\left( 2x+8 \right)={x}^{2}+12x+36$
Distribute $4$ through the parentheses$8x+32={x}^{2}+12x+36$
Move the expression to the left-hand side and change its sign$8x+32-{x}^{2}-12x-36=0$
Collect like terms$-4x+32-{x}^{2}-36=0$
Calculate the difference$-4x-4-{x}^{2}=0$
Factor out the negative sign from the expression and reorder the terms$-\left( {x}^{2}+4x+4 \right)=0$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression$-{\left( x+2 \right)}^{2}=0$
Change the signs on both sides of the equation${\left( x+2 \right)}^{2}=0$
The only way a power can be $0$ is when the base equals $0$$x+2=0$
Move the constant to the right-hand side and change its sign$x=-2$
Check if the given value is the solution of the equation$\sqrt{ -2+3 }=\sqrt{ 2 \times \left( -2 \right)+8 }-1$
Simplify the expression$1=1$
The equality is true, therefore $x=-2$ is a solution of the equation$x=-2$